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The recovery can be achieved from the undersampling signal in compressed sensing theory relying on the sparsity and incoherent characteristics of the signal. A data compression algorithm is advanced in this article, based on compressed sensing and wavelet transform. Firstly the framework of the compressed sensing theory is introduced, and then a one-dimension and a two-dimension wavelet transform matrixes are constructed respectively, which leads two compressed algorithms based on modulus and original data separately. At last, the compression characteristics are simulated and compared using one-dimension signal and two-dimension images separately, at the same time, the validity is proved by those results.